Unit 2 – Day 2 Name: Date: Integrated Math 4G: NOTES

Rational Expressions – Multiplying and Dividing Rational Expressions Today we will be simplifying rational expressions that are being either multiplied or divided by each other. We will use the same ideas as when we were just simplifying one fraction.

Ex 1) 𝑥2+5𝑥+6𝑥2−25

∙ 2𝑥+10𝑥2−9

For this first problem, we will go step-by-step. It is not necessary to write all of this out every time, but it is good to outline the process for the first one.

First we will factor all parts: Numerator 1: 𝑥2 + 5𝑥 + 6 Denominator 1: 𝑥2 − 25 Numerator 2: 2𝑥 + 10 Denominator 2: 𝑥2 − 9

Second we will put all the parts back:

∙

Last we will cancel all matches and write what is remaining:

Ex 2) 4𝑥2𝑦

2𝑤2𝑥3 ∙ 3𝑤6𝑦2 Don’t have to factor this one.

Why? Because it is all multiplication!

Ex 3) 𝑥+4𝑥2+6𝑥+9

∙ 𝑥2−93𝑥+12

Unit 2 – Day 2 When we divide rational expressions, it is just like multiplying, but first you must change it to multiplication by the reciprocal. I’ll refer to this as “KEEP, CHANGE, FLIP”.

Ex 4) 78

÷ 143

Ex 5) 𝑎2−𝑏2

𝑎+𝑏÷ 𝑎2

𝑎−𝑏

Ex 6) 3𝑥+6

𝑥2−3𝑥−10÷ 4𝑥+8

𝑥2−25

You Try:

Ex 7) 3𝑎4𝑏4𝑎3 ∙ 𝑐

9𝑏6 Ex 8) 7𝑥−21𝑥2−7𝑥−8

÷ 𝑥2−95𝑥2−5